Major General Hitchcock, Commissioner of Exchanges, is authorized and directed to offer Brigadier General Trimble, now a prisoner of warinFort McHenry,inexchangeforMajor White, who is held as a prisoner at Richmond. He is also directed to send forward the offer of exchange by Henry M. Warfield, Esq. of Baltimore, under a flag of truce, and give him a pass to City Point.
Abraham Lincoln
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necuhve Mansion Vastington amany layor Seneral Hitchcocks Commissioner of Cachanges, is anthonged and directed to offer Bingadier General Trin prisoner of warinFort Inctienny,inexchange now w Major White, who is held as a preises at Richmond Ite is also directed to vand forwards the offer of exchange by Stennyin. Warfield, Eag. of Baltimore, under aflag 11 mice, and give him apass to tity Point. Abrakan Sincolus
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43571 Bachington City January 10th 1864. Major General Architect, Commissioner of aivachangera is authorized and directed by ffeed Bngader General Trelmble, new a firemen of warinFert ncheryinexchangefor Mayor White, who held a a firemen at Hillmannd. He is aker conducted by end forward the offer of exchange by Henryin. Warfield, Lag. of Balthmore, under a flag of three, and five him afaies to City Bink. Abraham Lincoln
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2.2 数学教科书
一本包含方程式的微积分教科书。
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3.4 EXERCISES
For the following exercises, the givenfunctionsrepresent the position of a particle traveling along a horizontal line.
a. Find the velocity and accelerationfunctions.
b. Determine the time intervals when the object is slowing down or speeding up.
150. ( s(t) = 2t^3 - 3t^2 - 12t + 8 )
151. ( s(t) = 2t^3 - 15t^2 + 36t - 10 )
152. ( s(t) = rac{t}{1 + t^2} )
153. A rocket is fired vertically upward from the ground. The distance ( s )infeet that the rocket travels from the ground after ( t ) seconds is given by ( s(t) = -16t^2 + 560t ).
a. Find the velocity of the rocket 3 seconds after being fired.
b. Find the acceleration of the rocket 3 seconds after being fired.
154. A ball is thrown downward with a speed of 8 ft/s from the top of a 64-foot-tall building. After ( t ) seconds, its height above the ground is given by ( s(t) = -16t^2 - 8t + 64 ).
a. Determine how long it takesforthe ball to hit the ground.
b. Determine the velocity of the ball when it hits the ground.
155. The positionfunction( s(t) = t^2 - 3t - 4 ) represents the position of the back of a car backing out of a driveway andthendrivingina straight line,where( s ) isinfeet and ( t ) isinseconds. In thiscase, ( s(t) = 0 ) represents the time atwhichthe back of the car is at the garage door, so ( s(0) = -4 ) is the starting position of the car, 4 feet inside the garage.
a. Determine the velocity of the car when ( s(t) = 0 ).
b. Determine the velocity of the car when ( s(t) = 14 ).
156. The position of a hummingbird flying along a straight linein( t ) seconds is given by ( s(t) = 3t^3 - 7t ) meters.
a. Determine the velocity of the bird at ( t = 1 ) sec.
b. Determine the acceleration of the bird at ( t = 1 ) sec.
c. Determine the acceleration of the bird when the velocity equals 0.
157. A potato is launched vertically upward with an initial velocity of 100 ft/s from a potato gun at the top of an 85-foot-tall building. The distanceinfeet that the potato travels from the ground after ( t ) seconds is given by ( s(t) = -16t^2 + 100t + 85 ).
a. Find the velocity of the potato after 0.5 s and 5.75 s.
b. Find the speed of the potato at 0.5 s and 5.75 s.
c. Determine when the potato reaches its maximum height.
d. Find the acceleration of the potato at 0.5 s and 1.5 s.
e. Determine how long the potato isinthe air.
f. Determine the velocity of the potato upon hitting the ground.
158. The positionfunction( s(t) = t^3 - 8t ) gives the positioninmiles of a freight trainwhereeast is the positive direction and ( t ) is measuredinhours.
a. Determine the direction the train is traveling when ( s(t) = 0 ).
b. Determine the direction the train is traveling when ( a(t) = 0 ).
c. Determine the time intervals when the train is slowing down or speeding up.
159. The following graph shows the position ( y = s(t) ) of an object moving along a straight line.
a. Use the graph of the positionfunctionto determine the time intervals when the velocity is positive, negative, or zero.
b. Sketch the graph of the velocityfunction.
c. Use the graph of the velocityfunctionto determine the time intervals when the acceleration is positive, negative, or zero.
d. Determine the time intervals when the object is speeding up or slowing down.
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- a. Determine the direction the train is traveling when *s*(*t*) = 0. - b. Determine the direction the train is traveling when *a*(*t*) = 0. - c. Determine the time intervals when the train is slowing down or speeding up.
159. The following graph shows the position *y* = *s*(*t*) of an object moving along a straight line.
- negative, or zero. b. Sketch the graph of the velocityfunction. - c. Use the graph of the velocityfunctionto determine the time intervals when the acceleration is positive, negative, or zero. - d. Determine the time intervals when the object is speeding up or slowing down.
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Chapter 3 | Derivatives 273 3.4 EXERCISES For the following exercises, the givenfunctionsrepresent the position of a particle traveling along a horizontal line. a. Find the velocity and accelerationfunctions. b. Determine the time intervals when the object is slowing down or speeding up. 150. s(t) = 2t3 −3t2 −12t + 8 151. s(t) = 2t3 −15t2 + 36t −10 152. s(t) = t 1 + t2 153. A rocket is fired vertically upward from the ground. The distance s in feet that the rocket travels from the ground after t seconds is given by s(t) = −16t2 + 560t. a. Find the velocity of the rocket 3 seconds after being fired. b. Find the acceleration of the rocket 3 seconds after being fired. 154. A ball is thrown downward with a speed of 8 ft/ s from the top of a 64-foot-tall building. After t seconds, its height above the ground is given by s(t) = −16t2 −8t + 64. a. Determine how long it takesforthe ball to hit the ground. b. Determine the velocity of the ball when it hits the ground. 155. The positionfunction s(t) = t2 −3t −4 represents the position of the back of a car backing out of a driveway andthendrivingina straight line,where s isinfeet and t isinseconds. In thiscase, s(t) = 0 represents the time atwhichthe back of the car is at the garage door, so s(0) = −4 is the starting position of the car, 4 feet inside the garage. a. Determine the velocity of the car when s(t) = 0. b. Determine the velocity of the car when s(t) = 14. 156. The position of a hummingbird flying along a straight linein t seconds is given by s(t) = 3t3 −7t 2 2 2 ... 2 2 2 a. Use the graph of the positionfunctionto determine the time intervals when the velocity is positive, negative, or zero. b. Sketch the graph of the velocityfunction. c. Use the graph of the velocityfunctionto determine the time intervals when the acceleration is positive, negative, or zero. d. Determine the time intervals when the object is speeding up or slowing down. 157. A potato is launched vertically upward with an initial velocity of 100 ft/s from a potato gun at the top of an 85-foot-tall building. The distanceinfeet that the potato travels from the ground after t seconds is given by s(t) = −16t2 + 100t + 85. a. Find the velocity of the potato after 0.5 s and 5.75 s. b. Find the speed of the potato at 0.5 s and 5.75 s. c. Determine when the potato reaches its maximum height. d. Find the acceleration of the potato at 0.5 s and 1.5 s. e. Determine how long the potato isinthe air. f. Determine the velocity of the potato upon hitting the ground. 158. The positionfunction s(t) = t3 −8t gives the positioninmiles of a freight trainwhereeast is the positive direction and t is measuredinhours. a. Determine the direction the train is traveling when s(t) = 0. b. Determine the direction the train is traveling when a(t) = 0. c. Determine the time intervals when the train is slowing down or speeding up. 159. The following graph shows the position y = s(t) of an object moving along a straight line. 155. The position of a hummingbird flying along a straight linein t seconds is given by s(t) = 3t3 −7t 2 2 3 3 3 ..... 125.5 126 126.5
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a. Determine the direction the train is traveling when$s(t)=0$ . b. Determine the direction the train is traveling when$a(t)=0$ . c. Determine the time intervals when the train is slowing down or speeding up.
159. The following graph shows the position$y=s(t)$ of an object moving along a straight line.
a. Use the graph of the positionfunctionto determine the time intervals when the velocity is positive, negative, or zero. b. Sketch the graph of the velocityfunction. c. Use the graph of the velocityfunctionto determine the time intervals when the acceleration is positive, negative, or zero. d. Determine the time intervals when the object is speeding up or slowing down.
4. The natives soon had reason to suspect the viceroy's sincerity in his expressions of regret at the proceedings of which they complained. For about this time the Dominican friars, under pretence of building a convent, erected a fortress on the island of Solor, which, as soon as finished, the viceroy garrisoned with a strong force. The natives very naturally felt indignant at this additional encroachment, and took every opportunity to attack the garrison. The monks, forgetful of their peaceable profession, took an active part in these skirmishes, and many of them fell sword in hand.
The Mahomedan faith has been appropriately entitled, The religion of the sword; and with equal propriety may we so designate the religion of these belligerent friars. The Portuguese writers give an account of one of their missionaries, Fernando Vinagre, who was as prompt in the field of battle as at the baptismal font. This man, though a secular priest, undertook the command of a squadron that was sent to the assistance of the rajah of Tidore, on which occasion he is said to have acted in the twofold capacity of a great commander, and a great apostle, at one time appearing in armour, at another in a surplice; and even occasionally, baptizing the converts of his sword without putting off his armour, but covering it with his ecclesiastical vest. In this crusade he had two
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## **IN INDIA *** BOOK TI. S69 Christians behaving themselves like Ma borne- a. dans.3 . extquotedblleft5/0- *t>.*
The natives soon had reason to suspect the viceroy, viceroy's sincerity in his expressions of regret at the proceedings of which they complained. extquotedblleft n. extquotedblleft'For about this time the Dominican friars, under pretence of building a. convent, erected a fortress on the island of Sol or,which, as soon as finished, the viceroy garrisoned with a strong force. The natives' very naturally felt indig-S nant at this additional encroachment, and took every opportunity to attack the garrison. The monks, forgetful/ of their peaceable profession, took an active part in these skirmishes, and many of tbg.tr fell sword in hand.
The i'lfinomedan faith has been appropriately entitled., extquoteleft The religion of the sword extquoteright,; and with equal propriety may we so designate the re- . i'gv.m of these belligerent friars. The Portugu writers give an account of one of their extquoteleft missionaries, extquoteright Fernando Vinagre, who was as prompt in the field of battle as at the baptismal font. This man, though a secular priest, undertook the command of a squadron that was I sent to the assistance of the rajah of Tidore,4 on which occasion he is said to have acted in the twofold capacity of a great commander, and a great apostle, at one time appearing in armour, ; at another in a surplice; and even occasionally, baptizing the converts of his sword without putting off his armour, but covering it with his ecclesiastical vest. In this crusade5 he had two > 3 Geddes History, &c., pp. 24---27. Pudet hae c opprobria nobis Vel dici potuisse. > 4 Called extquoteleft T a d u ra extquoteright or extquoteleft D a c o, extquoteright an island in the Indian Ocean, one of the Moluccas > 5 extquoteleft These extquoteleft a la D ra g o o n extquoteright conversions. extquoteright Geddes'History, p. 27.
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IN INDIA: BOOK U 269 Christians behaving themselves like Mahome- 1670. 4. The natives son had reason to suspect the Viceroy' s vice roy's sincerityinhis expressions of regretinsine eri ty at the proceedings ofwhichthey complained. fl it ars. For about this time the Dominican f mars, under pre ten ce of building a convent, erected afor- tress on the island of Sol or,which, as soon as finished, the vice roy garrisoned with a strong force. The natives very naturally felt indig- nant at this additional encroachment, and took every opportunity to attack the garrison. The monks, forgetful of their peaceable profession, took an active partinthese skirmishes, and many of the n fell swordinhand. The Mh on med an faith has been appropriately entitled. The religion of the sword; and with e ral Tropriety may we so designate the re- gian of these belligerent friars. The Port u- gue s writers give an account of one of their mission are s, Fer endo Vina gre, who was as promptinthe fe ld of battle as at the baptismal font. This man, though a secular priest, un- der took thecommandof a squadron that was sent to the assistance of the rajah of Tidore, onwhichoccasion he is said to have actedinthe twofold capacity of a great commander, and a great apostle, at one time appearinginarmour, at anotherina surplice; and even occasionally, baptizing the converts of his sword without put- ting off his armour, but covering it with his ecclesiastical vest. In this crusade he had two 3 Ged des History, & c. , pp. 24-27. P ude th aec opp rob ria nobis Vel die ipo tui sse. Called Tadur u or Daco, an islandinthe Indian Ocean, one of the Mol ucc as These a laDra goon conversions. Ged des History, p. 27.
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ININDIASY BOOKU Christians bchaving.themselves like Mahome dans.3
4.The natives soon had reason to suspect ihe viceroy's sincerity in his expressions of regret at the proceedings of which they complained. For about this time the Dominican friars,under pretenceof building a convent,erected a for tress on the island of Solorwhich,as soon as finishedthe viceroy garrisoned with a strong force. The natives very naturally felt indig nant at this additional encroachment, and took every pportunity to attack the garrison.The monks,forgetful of their peaceable profession took an activa part in these skirmishes, and many of tbein feil sword in hand.
TheMahornedan faithhas been appropriately ntitled.The religion of the swordand with equal propriety may we so designate the region of these belligerent friars.The Portugueswriters give an account of one of their missionarzes,femando Vinagre,who was as prompt in the field of battle as at the baptismal font. This man, though a secular priest, undertook the command of a squadron that was sent to the assistance of the rajah of Tidore,4 on which occasion he is said to have acted in the twofold capacity of a great commander, and a great apostle, at one time appearing in armour, at another in a surplice;and even occasionally baptizing the converts of his sword without put ting off his armour, but covering it with his ecclesiastical vest.In this crusadehe had two
